12 research outputs found
Symmetries in M-theory: Monsters, Inc
We will review the algebras which have been conjectured as symmetries in
M-theory. The Borcherds algebras, which are the most general Lie algebras under
control, seem natural candidates.Comment: 6 pages, talk given by PHL at Cargese 200
Maximal supergravity in D=10: forms, Borcherds algebras and superspace cohomology
We give a very simple derivation of the forms of supergravity from
supersymmetry and SL(2,\bbR) (for IIB). Using superspace cohomology we show
that, if the Bianchi identities for the physical fields are satisfied, the
(consistent) Bianchi identities for all of the higher-rank forms must be
identically satisfied, and that there are no possible gauge-trivial Bianchi
identities () except for exact eleven-forms. We also show that the
degrees of the forms can be extended beyond the spacetime limit, and that the
representations they fall into agree with those predicted from Borcherds
algebras. In IIA there are even-rank RR forms, including a non-zero
twelve-form, while in IIB there are non-trivial Bianchi identities for
thirteen-forms even though these forms are identically zero in supergravity. It
is speculated that these higher-rank forms could be non-zero when higher-order
string corrections are included.Comment: 15 pages. Published version. Some clarification of the tex
The general gaugings of maximal d=9 supergravity
We use the embedding tensor method to construct the most general maximal
gauged/massive supergravity in d=9 dimensions and to determine its extended
field content. Only the 8 independent deformation parameters (embedding tensor
components, mass parameters etc.) identified by Bergshoeff \textit{et al.} (an
SL(2,R) triplet, two doublets and a singlet can be consistently introduced in
the theory, but their simultaneous use is subject to a number of quadratic
constraints. These constraints have to be kept and enforced because they cannot
be used to solve some deformation parameters in terms of the rest. The
deformation parameters are associated to the possible 8-forms of the theory,
and the constraints are associated to the 9-forms, all of them transforming in
the conjugate representations. We also give the field strengths and the gauge
and supersymmetry transformations for the electric fields in the most general
case. We compare these results with the predictions of the E11 approach,
finding that the latter predicts one additional doublet of 9-forms, analogously
to what happens in N=2, d=4,5,6 theories.Comment: Latex file, 43 pages, reference adde
Zero-Branes, Quantum Mechanics and the Cosmological Constant
We analyse some dynamical issues in a modified type IIA supergravity,
recently proposed as an extension of M-theory that admits de Sitter space. In
particular we find that this theory has multiple zero-brane solutions. This
suggests a microscopic quantum mechanical matrix description which yields a
massive deformation of the usual M(atrix) formulation of M-theory and type IIA
string theory.Comment: 15 pages LaTeX, added reference
Forms and algebras in (half-)maximal supergravity theories
The forms in D-dimensional (half-)maximal supergravity theories are discussed
for 3 D 11. Superspace methods are used to derive consistent sets
of Bianchi identities for all the forms for all degrees, and to show that they
are soluble and fully compatible with supersymmetry. The Bianchi identities
determine Lie superalgebras that can be extended to Borcherds superalgebras of
a special type. It is shown that any Borcherds superalgebra of this type gives
the same form spectrum, up to an arbitrary degree, as an associated Kac-Moody
algebra. For maximal supergravity up to D-form potentials, this is the very
extended Kac-Moody algebra E11. It is also shown how gauging can be carried out
in a simple fashion by deforming the Bianchi identities by means of a new
algebraic element related to the embedding tensor. In this case the appropriate
extension of the form algebra is a truncated version of the so-called tensor
hierarchy algebra.Comment: 59 pages, 1 figur